For general AOEs, I've not had an issue when using a controller, and I play on an American datacentre while living in Europe. Might we worth trying it out with a controller? You say that it's usually fine, but you should be able to step outside of the vast, vast majority of AOEs.
The main reason that the Drop Dead DRG is a thing is because of Jump attacks. You can never know when a boss is about to drop an AOE on you, and the animation lock for the Jump attacks is such that after you launch, the AOE can drop, and by the time you land back down and try to get out of the AOE, it's too late.
That's just the way the job works in the game. You can only try to mitigate it so much before you're losing DPS, so it's better to take the damage, hope you survive it, and let a healer fix you up.